Second, I could see them opening an eastern front against the Habsburgs in the War of the Spanish Succession.
You are seemingly ignoring the fact that in the PLC the royal power was quite limited, to put it mildly. The chances that Conti would be able to convince the Sejm to start a war against the traditional ally (the Hapsburgs) just to benefit the King of France would be extremely slim. IIRC, Sejm even financing of the Great Ottoman War was problematic, especially on the late stage.
At best, Conti could try to pull the PLC out of the Great Ottoman War by making a separate peace. Not that at this stage it would matter much for anybody besides the Poles. Then, of course, goes a sad fact that by the time in question the PLC almost ceased to exist as a noticeable military power: during the GNW the Russians, Saxons and Swedes had been fighting on it territory even when the PLC was neutral and on the rare occasions when the the PLC troops did participate in the battles their performance was quite unimpressive. As Swedish general Mardefelt pointed out before the Battle of Kalisz, the Poles had not been keen on fighting Russians or anyone at all during the war (and he proved to be correct: as soon as the Russian troops advanced, the crown army led by
Józef Potocki fled from the field).
In the long term, Prince Conti and his successors, with French help, may have been able to resist the partitions.
This assumes 2 things: (a) that Conti manages to establish a dynasty and (b) that France could provide any realistic help to the PLC by the late XVIII. None of them (IMO) has too much traction with a reality. Russia and Hapsburgs had much more weight in the region (and much better communications) and, as was demonstrated by the War of the Polish Succession, France could do close to nothing in the PLC to help its candidate. The same goes for the Partitions: what France could do in the practical terms against the combination of Russia, Prussia and Hapsburgs?